caa a22 4500 463196600 CHVBK 20180406164924.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s10773-007-9364-8 doi (NATIONALLICENCE)springer-10.1007/s10773-007-9364-8 Conceptual Unification of Gravity and Quanta [Elektronische Daten] [Michael Heller, Leszek Pysiak, Wiesław Sasin] We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra $\mathcal{A}$ on the groupoid Γ=E×G where E is the total space of the frame bundle over spacetime, and G the Lorentz group. The differential geometry, based on derivations of $\mathcal{A}$ , is constructed. The eigenvalue equation for the Einstein operator plays the role of the generalized Einstein's equation. The algebra $\mathcal{A}$ , when suitably represented in a bundle of Hilbert spaces, is a von Neumann algebra ℳ of random operators representing the quantum sector of the model. The Tomita-Takesaki theorem allows us to define the dynamics of random operators which depends on the state φ. The same state defines the noncommutative probability measure (in the sense of Voiculescu's free probability theory). Moreover, the stateφ satisfies the Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a generalized equilibrium state. By suitably averaging elements of the algebra $\mathcal{A}$ , one recovers the standard geometry of spacetime. We show that any act of measurement, performed at a given spacetime point, makes the model to collapse to the standard quantum mechanics (on the groupG). As an example we compute the noncommutative version of the closed Friedman world model. Generalized eigenvalues of the Einstein operator produce the correct components of the energy-momentum tensor. Dynamics of random operators does not "feel” singularities. Springer Science+Business Media, LLC, 2007 Heller Michael Vatican Observatory, 00120, Vatican, Vatican aut Pysiak Leszek Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut Sasin Wiesław Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/10(2007-10-01), 2494-2512 0020-7748 46:10<2494 2007 46 10773 https://doi.org/10.1007/s10773-007-9364-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9364-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Heller Michael Vatican Observatory, 00120, Vatican, Vatican aut NATIONALLICENCE 700 1- Pysiak Leszek Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut NATIONALLICENCE 700 1- Sasin Wiesław Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/10(2007-10-01), 2494-2512 0020-7748 46:10<2494 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer